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Mathematical modeling of delayed pertussis vaccination in infants P. Pesco a , P. Bergero a , G. Fabricius a,∗ , D. Hozbor b a Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, CC 16, Suc. 4, 1900 La Plata, Argentina b Laboratorio VacSal, Instituto de Biotecnología y Biología Molecular, Departamento de Ciencias Biológicas, Facultad de Ciencias Exactas, Universidad Nacional de La Plata y CCT-La Plata, CONICET, Calles 47 y 115, 1900 La Plata, Argentina
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Article history: Received 30 March 2015 Received in revised form 26 June 2015 Accepted 1 July 2015 Available online xxx Keywords: Pertussis Resurgence Delay in vaccination Mathematical model
a b s t r a c t Pertussis is an acute vaccine-preventable respiratory disease that remains a public health problem. In an attempt to improve the control of the disease, many countries have incorporated new boosters in their vaccination schedule. Since the incorporation of these boosters is relatively recent, there are not enough data about their impact to support and/or universalize their use. Alternative strategies such as the improvement in vaccine coverage and reduction in vaccination delays, in addition to the incorporation of boosters, could be implemented. Though these strategies are not new, they have not been adequately evaluated in order to be implemented and/or prioritized. To evaluate the potential impact of these alternative strategies on pertussis incidence, we developed a methodology that involves the use of data collected from vaccination centers and an age-structured deterministic mathematical model for pertussis transmission. The results obtained show that strategies that avoid delays in vaccination have a strong impact on incidence reduction in the most vulnerable population (infants less than 1y). In regions with high vaccination coverage (95%) the elimination of delays in the three primary doses decreases pertussis incidence in infants by approximately 20%. In regions where delays in the administration of vaccines are higher, the combined action to reduce delays and improve coverage leads to a significant improvement in disease control in infants. By repeating the calculations using different sets of parameters that describe different possible epidemiologic scenarios, we determined the robustness of our results. All the results presented highlight the importance of having high vaccine coverage and shorter delays in vaccine administration in order to reduce the impact of the disease in infants. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Pertussis is a highly contagious respiratory disease mainly caused by Bordetella pertussis. This disease, which causes uncontrollable violent coughing, most commonly affects infants and young children and can be fatal, especially in babies less than 1 year of age [1,2]. The best way to prevent pertussis is to get vaccinated. In fact, the introduction of massive pertussis vaccination in the fifties dramatically reduced the morbidity and mortality associated with the disease. However, in the last years the incidence rates of the disease have increased in many countries [3–6]. The World Health Organization estimates that about 16 million cases occur per year in the world with approximately 200,000 deaths [7]. Though most of these cases have been reported in countries with low
∗ Corresponding author. Tel.: +54 2214257430; fax: +54 2214254642. E-mail address: fabricius@fisica.unlp.edu.ar (G. Fabricius).
vaccination coverage, pertussis outbreaks were also detected in countries with high vaccination coverage [3,4]. In the Americas, the number of cases varies between 1500 and 49,000 among countries, where Argentina, Brazil, Mexico, Chile, Colombia, Paraguay, Peru, and the United States have reported the highest number of cases [8–10]. In Argentina, the last outbreak occurred in 2011 when 76 deaths were reported mainly in children under 6 months [11]. In 2012, in the US 48,778 cases (the highest outbreak since 1955) including 20 pertussis-related deaths were reported. Incidence rates were very high in infants but also in the population of children (7–10 years) and adolescents (13–14 years) [12]. This epidemiological situation has forced health systems to revise their control actions to strengthen and/or implement shortterm strategies to improve the situation, at least for the most vulnerable population represented by infants. Before the resurgence of the disease, recommended immunization schedules consisted of a primary series of 3 doses during the first year of life and a booster between 1 and 6 years of age, preferably during the second year of age. With the disease resurgence, more boosters
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were added following recommendations of international organizations [13–15]. In fact, the number of boosters increases year by year in many countries, probably as a consequence of failures in the used vaccines, in particular in acellular vaccines [16,17]. In this context, the evaluation of other alternative strategies, instead of the addition of the current acellular booster doses, is important for controlling the disease in the short term. In previous work, using an age-structured deterministic mathematical model for pertussis transmission designed by us, we estimated that improvements in the coverage of the first dose would lead to a larger reduction in the 0–1y disease incidence than that caused by the addition of an 11y booster [18]. The population dynamics of our model was described by transferring individuals among 9 epidemiological classes that differ in immune status and infectiousness. In the present work we evaluate the potential impact of shorter delays in the administration of the first three doses of pertussis vaccine on infants younger than 1y. With this aim, we developed a calculation method that involves the introduction of new epidemiological classes to keep track of the number of doses administered to the population in each epidemiological class. This method also allows us to accurately incorporate the vaccination coverage for each dose in the model. The results obtained with our model and data gathered from vaccination centers in urban and suburban areas in an Argentine city show that a reduction in delayed vaccination would decrease the incidence of the disease in infants by at least 20%. The results from the model reveal that efforts to improve the administration of the first doses of the immunization schedule, either by enhancing coverage or strictly complying with the recommended scheduled age, would significantly decrease pertussis incidence in infants. 2. Materials and methods 2.1. Vaccination schedule and epidemiological data In Argentina, the immunization schedule against pertussis includes three primary doses at 2, 4 and 6 months old, one booster dose at 18 months old, and another at 6 years (school entry) [19]. For all these doses, whole-cell pertussis vaccine is used (DTwP). According to the Ministry of Health, DTP3 coverage (DTP3-cov) for infants under 1y old was higher than 90%, but there are some regions with coverage below 80% [11]. Over the last few years, since the resurgence of pertussis, different protection strategies have been included in Argentina: immunization of adolescents, pregnant women and health workers with acellular vaccines. The epidemiological data included in this work, consisting of 29,845 records of pertussis vaccination for children aged 0–12 months, are from La Plata (654,324 inhabitants), an Argentinian city located in Buenos Aires province. Specifically, we used retrospective data (January 2005–May 2012) on the distribution of applied DTP doses by age provided by the vaccination center of Elina de la Serna Hospital. At this center, which is one of the 10 vaccination centers located in the urban region of La Plata city, approximately 13% of La Plata population is vaccinated. Children whose age was undefined or unclear were excluded. Fig. 1A shows the number of vaccinated individuals per dose by age from January 2005 to May 2012. In Fig. 1B we represent the same data as in Fig A, but as a fraction of vaccinated individuals at age ai with dose d (hereafter referred to as fdi ). These profiles were obtained by performing histograms with the data of Fig. 1A, where each histogram interval is taken as a month divided by four (a “week”), ages ai are assigned to the middle of the interval, and fdi are normalized to one for each dose, d. The fdi profiles and the vaccination coverages for each dose DTP-covd are the parameters that determine vaccine administration in our mathematical model.
Fig. 1. (A) Number of vaccinated individuals per dose by age, between January 2005 and May 2012 (continuous lines). Data are from Elina de la Serna Hospital. (B) Fraction of vaccinated individuals with dose d, at age ai (in weeks), fdi (gray lines are to guide the eye). Data are obtained from (A). In both figures dotted lines indicate the recommended age for primary doses of pertussis vaccination schedule in Argentina.
For comparison purposes, we also included epidemiological data from the periphery of La Plata city, where the population is younger than that from downtown, with 23% and 14% of inhabitants younger than 14 years old, respectively. There are 3.7 individuals per household on average, instead of the 2.7 individuals registered in the downtown area [20]. 2.2. Mathematical model The model used here to evaluate the effect of vaccination delays on pertussis transmission is based on a deterministic agestructured compartmental model developed previously by us [18]. The population dynamics of this model is described transferring individuals among 9 epidemiological classes at given rates as is shown in Fig. 2A. Each one of the 9 epidemiological classes is divided into age groups. To study the effect of delays in vaccination we have introduced modifications into the model that allow us to take into account the actual age at which the population receives the three primary doses of the pertussis vaccine, regardless of the age recommended by the national vaccination schedule. On the other hand, the fact that vaccination does not have a 100% effectiveness is considered assuming that only a fraction of
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Fig. 2. (A) Schematic representation of the basic epidemiological model. Individuals are born in the susceptible class S and remain there unless they become infectious through contact with an infected individual and enter the full symptomatic infective class I1 , or they acquire the lowest level of immunity (via the application of the first effective vaccine dose) and enter P1AI (PAI : Partial Acquired Immunity). When receiving successive effective vaccination doses (dotted lines), individuals go through classes of increasing immunity and eventually reach the CAI (Complete Acquired Immunity) class. Individuals in classes P1AI and P2AI develop a less symptomatic illness when they get infectious, entering class I2 (mild infection) or I3 (weak infection), respectively. Infection fades at a rate ␥ and individuals in classes I1 , I2 or I3 recover and enter R class. Waning immunity is considered by transferring population from classes R, CAI or PAI to classes of lower immunity at rates , , , respectively. Each epidemiological class is divided into age groups. (B) Disaggregation of S and PAI classes by applied doses. The subindex indicates the number of applied doses. The superindex in PAI classes determines the immunity level of the class and corresponds to the number of effective doses. Arrows represent population transfers when an effective (vertical) or ineffective (horizontal) dose of vaccine is applied. This increase in the number of epidemiological classes holds for age groups from 0 to 1y. For people older than 1y, discrimination of the population by the number of applied doses is not necessary and 9 epidemiological classes as in (A) are considered.
the individuals that received one dose of vaccine is transferred to an epidemiological class with a higher level of immunity. The rest of the individuals that after receiving the extra dose did not modify their immunological status are transferred to a new class that comprises a population of individuals with the same status of immunity but with an additional dose. In the previous model [18], when the dose was not effective, the individual remained in the original epidemiological class and no records of the number of doses administered were kept. Here this discrimination of transfer to another epidemiological class is necessary since the second dose is only given to individuals who have already received the first one (and the same for the third dose with respect to the second). The new compartments added to the model to account for this effect are shown in Fig. 2B. When an effective dose d is given at age ai , a fraction pdi *VE (of those moved due to aging) is transferred to an increased immunity class (indicated with vertical arrows in the figure). If the dose d is ineffective, a fraction pdi *(1-VE) is transferred to a class with the same level of immunity and one more dose given (horizontal arrow), while a fraction 1-pdi does not receive the dose and remains in the same class. Here, VE is the vaccine efficacy, pdi is the fraction of the aged ai population with d-1 doses that receives dose d at age ai , and is obtained from the fraction of vaccinated individuals by age fdi , and the corresponding vaccination coverage, DTPd-cov (computed as the fraction of infants vaccinated before 1y old). The set of ages ai is taken weekly from 2m to 1y (we assume each month has 4 weeks, a detailed explanation of the implementation of the vaccination procedure in the model is presented in the Supplementary Material). The dynamics of the model is described by a set of coupled nonlinear differential equations that are solved numerically to obtain the stationary state of the system. The incidences of the disease are then computed through expressions Inc1i = i (Si + S1i + S2i + S3i ),
1 1 1 Inc2i = i (PAI1 i + PAI2i + PAI3i )
where Inc1i and Inc2i are the incidences of fully and mild symptomatic pertussis cases, respectively for age group i. Inc1i is computed as the product of the force of infection i and the total population of susceptible individuals in the corresponding age group, which is composed of unvaccinated individuals (Si ) and vaccinated individuals with 1, 2 or 3 doses of vaccine that have been ineffective for them (S1i , S2i , S3i , respectively). Inc2i is computed in the same way, but the population considered is in the first
acquired immunity class as they have received 1 effective dose of vaccine. 3. Results For all calculations presented here, we considered the parameters corresponding to a previously defined CP1A-MDI scenario (see Ref. [18], where contact parameters obtained from forces of infection in the pre-vaccine era and intermediate values reported for the duration of pertussis immunity are considered). In the Supplementary Material, the complete set of parameters used in this work is presented, and the results obtained for other scenarios are discussed. 3.1. Assessment of the effect of delayed vaccination for different coverages The aim of this work is to assess the impact on the pertussis incidence in infants due to the reduction in the delays in DTP vaccination. With this purpose, we compared the incidences predicted by the model when the vaccination is delayed and when the recommended vaccination schedule is adhered to without any delay. To compute the 0–1y incidences in the case of delayed vaccination in our model, we included the weekly vaccination profile shown in Fig. 1B, and considered two possible values for DTP3-cov: 95% and 80%. To reach these coverages, we assume that DTP1-cov > DTP2-cov > DTP3-cov. We arbitrarily consider two sets: DTP1-cov = 99%, DTP2-cov = 97% DTP3-cov = 95%, and DTP1cov = 90%, DTP2-cov = 85%, DTP3-cov = 80%. As there are other possible combinations of coverages to reach the same DTP3-cov, we repeated the calculations for the case that all individuals that receive DTP1 also receive the following doses (DTP1-cov = DTP2cov = DTP3-cov, see Supplementary Material). Fig. 3 shows the incidences in the 0–1y group considering a delay in vaccination and the ideal situation without delay. As expected, when DTP3-cov = 95% and without delay, the predicted incidences are the lowest. When the delay is considered, both Inc1 and Inc2 increase. A similar trend is observed when DTP3cov = 80%. It should be noted that although no delayed vaccination is an unreal situation, the strategy of evolving from a stage DTP3cov = 80% with delay to a stage DTP3-cov = 95% without delay results in an incidence (Inc1 + Inc2 ) reduction of 39% with respect to the initial situation.
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8.4
Not Delayed
Delayed
14.2
0 DTP3-cov = 95%
Not Delayed
Delayed
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3
3.2. Assessment of some strategies for delay reduction In this section we evaluate different strategies to diminish the delays detected in the urban region (Fig. 1B, case I). For these calculations we considered DTP3-cov = 95%, as was reported for different urban areas of our country by Gentile et al. [23]. We first assessed the effect of completely avoiding the delay in the first dose (case II). The calculation shows that Inc1 + Inc2 remains as in case I (19.7 cases/year/100,000 inhabitants). However, reducing Inc1 (7.4 in case II instead of 8.4 in case I) at the expense of Inc2 (12.3 in case II vs. 11.3 in case I) decreases the number of severe pertussis cases. We also assessed the effect of avoiding the cumulative delays in DTP2 and DTP3 (case III). Here DTP1 is administered with delay, but with strict compliance with the recommended interval (2 months) between the following doses. As a result, Inc1 + Inc2 decreases by 13.9% with respect to case I, while a minor change for Inc1 results (3.3%). In case IV, DTP1 dose is administered as in case I, but the following doses are given without any delay, at the minimum interval between consecutive doses recommended by WHO. In this situation, as expected, the predicted Inc1 + Inc2 is slightly lower than that for case III (16.7 in case IV vs. 17.0 in case III) but higher than that for case V (16.7 in case IV vs. 16.2 in case V). Case V corresponds to no delayed vaccination, in which Inc1 and Inc2 decrease with respect to case I by 16.3% and 19%, respectively. This improvement is even higher (49.6% for Inc1 and 19% for Inc2 ) if only the 2–12m group, which is the one susceptible to be directly affected by vaccination, is considered (Table 1). 3.3. Assessment of the effect of changing the vaccination profile of a suburban area to that of an urban area In the suburban area of La Plata we detected a different vaccination profile with greater delays. The detail of the data is included in the supplementary material (Fig. S4). In Fig. 4 we show the agespecific coverage of DTP3 for the urban and suburban areas of La Plata and also include the ones for Flanders (Belgium) [21] and Armenia [22] to show that the delays detected in other regions are similar to those found in La Plata, or they could be even greater. To estimate the effect of the suburban-area delays on 0–1y pertussis incidence, we consider that the coverage for DTP3 is 87% instead of the 95% that we took for the urban area. We assume
La Plata (urban) La Plata (suburban) Flanders Armenia
0.2 0.1 0 100
DTP3-cov = 80%
Fig. 3. Effect of the delay on incidences Inc1 and Inc2 for DTP3-cov 95% and 80%. The numbers inside the bars indicate the Inc1 and Inc2 values, and the numbers above correspond to Inc1. + Inc2 . The label “Delayed” corresponds to the profile of Fig. 1(B), while the label “not delayed” corresponds to the case where all individuals receive the first, second and third vaccination doses at 2m, 4m and 6m, respectively.
3th dose
150
200
250
300
350
400
450
500
Age of immunization with DTP3 (days) Fig. 4. Age-specific coverage for DTP3 in La Plata, Argentina (urban and suburban areas). Data from Flanders (Belgium) [21] and Armenia [22] are shown for comparative purposes. The vertical line indicates the age of immunization recommended by the Argentinean and Armenian National Vaccination Schedules. The curve for Belgium was shifted 2 months to superimpose on the recommended age of vaccination in the other countries. La Plata urban data were obtained from Fig. 1(A), assuming DTP3-cov = 95%. For the suburban curve we included 1764 records of DTP vaccinations in infants between 0 and 12 months old obtained from Public Health Centers on the outskirts of La Plata (December 2012 and March 2013), assuming DTP3-cov = 87%.
DTP3-cov = 87% since from the information recorded in several vaccination centers of the suburban region, we found that 13% of the children who had completed their DTP3 vaccination dose received the third dose between 1 year and 3 years of age. Then, assuming that at the age of three 100% of the children received the DTP3 dose, at 1 year of age only 87% of the children have received the three recommended pertussis vaccine doses. If we assume that the proportions in such records are preserved in the whole suburban population, DTP3-cov should be at most 87%. The results of our calculations are shown in Fig. 5. When the delays in vaccination were reduced from those in the suburban profile (DTP3-cov = 87%) to the ones in the urban profile (DTP3-cov = 95%) of La Plata, a 27% decrease in Inc1 + Inc2 , 35.1% in Inc1 , and 19.5% in Inc2 was observed. In the figure we also included the results obtained for two other coverages for the suburban area: 80%, because this value can
Incidence (Cases/year per 100,000 population)
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13.5
10 13.0
5 0
DTP3−cov
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15.9
10.2
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87%
80%
Fig. 5. Comparison of incidences Inc1 and Inc2 for the 0–1y age group for urban and suburban vaccination profiles of La Plata. DTP3-cov = 95% was used for the urban profile, while for the suburban profile three different DTP3-cov values were considered: DTP3-cov = 95% (higher than expected from the data), DTP3-cov = 87% (upper limit supported by current data) and the more realistic DTP3-cov = 80%. When DTP3cov = 87% we take DTP1-cov = 94.5% and DTP2-cov = 91%. For the other cases, we take the same coverages as in Section 3.1 for the first 2 doses.
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Table 1 Effect of the delay in the incidence by age for infants with less than 1y. Comparison of Inc1 and Inc2 values between delayed (Case I, Fig. 1(B)) and not delayed (Case V, Section 3.2) vaccination using DTP3-cov = 95%. DTP3-cov 95%
Inc1 Cases/year per 100,000 population
Age (m)
Delayed Case I
Not delayed Case V
Delayed Case I
Not delayed Case V
0–2 2–4 4–6 6–12 0–12
5.7 1.4 0.7 0.6 8.4
5.7 0.6 0.3 0.5 7.1
0.0 4.2 4.5 2.6 11.3
0.0 5.0 2.4 1.7 9.1
Inc2 Cases/year per 100,000 population
be detected in this region, as was reported by Gentile et al. [23], and 95%, which although not being realistic, from an academic point of view, it is interesting to separately observe the effects of coverage and delays when comparing them with those of the urban profile. The decrease in incidence predicted by the model in changing from a suburban to an urban profile was more pronounced than that resulting from the reduction in the urban profile up to fully compliance with the immunization schedule. In the Supplementary Material we discuss the robustness of our results considering different scenarios including the duration of immunity, the contact matrix, and vaccine effectiveness. 4. Discussion For pertussis and other vaccine-preventable diseases, the delay in the acquisition of immunity through late immunization could negatively impact on the disease transmission [24–27]. In fact, it is generally accepted that immunization at the earliest appropriate age is an important public health goal. Several countries such as US, Sweden and Australia have reported age properly immunized around 48–75% [28]. In Argentina, delay in vaccination was also detected in different populations [29–31]. The impact of delayed vaccination on the incidence of pertussis has been scarcely studied, and the effect of reducing it is even less known [24,32]. In this work, we assessed the impact on the incidence in the most vulnerable group due to the reduction in the delays of the primary doses of pertussis vaccine. With this aim, we used an age-structured deterministic mathematical model for pertussis transmission and data collected from an urban vaccination center in Argentina. With our model, we evaluated the impact of completely avoiding the delays in each one of the three recommended primary doses for pertussis control. The results show that incidence reduction is important for both analyzed coverage: 95% (adequate) and 80% (suboptimal), being more noticeable in the first coverage scenario. Avoiding delays in the administration of primary doses would have a different impact on the 0–2m group than on the 2–12m group. As expected, in the 0–2m group the impact of reducing the delays is hardly noticeable (only reduction due to herd immunity, which in this case is low) since this age group is not given any vaccine according to immunization schedules like that of Argentina. For the 2–4m group no delays decrease the number of severe cases (Inc1 decreases by 56.4% for 95% coverage) and for the 4–6m and the 6–12m groups with 95% coverage, Inc1 + Inc2 decreases up to 48.5% and 31.1%, respectively. Although this reduction in delayed vaccination up to full compliance with the immunization schedule seems highly unlikely due to the numerous uncontrollable reasons that may cause it [29,31], our results point out the magnitude of the improvement that could be achieved by implementing such health-care actions. Our method also allowed us to analyze other strategies that could be more easily implemented by the health system. Thus, we observed that when there are no delays in DTP1 administration, although the total incidence cannot be decreased,
the total number of severe cases is lower (lower Inc1 at the expense of Inc2 ). This strategy should be recommended by pediatricians to newborns’ parents. Moreover, when delays are not cumulative (i.e., when after the first dose the 2 month interval is strictly preserved) Inc1 + Inc2 decreases by 13.8%. Comparatively, the elimination of the vaccination delays in both the second and third doses causes a smaller effect on incidence reduction, mainly affecting the Inc2 value. This strategy should be mainly recommended by vaccinators. We could also observe that when the delay in suburban areas could be reduced to those in the urban area, a reduction of 27% in Inc1 + Inc2 could be detected. Although the delays and profiles we worked with are from Argentina, they are comparable to those in other countries, as shown in Fig. 4. The robustness of our results was tested by repeating the calculations using different sets of parameters allowing us to extend our conclusions to other possible epidemiological scenarios (Supplementary material). All these results undoubtedly show that the reduction in the delays has a positive impact on incidence reduction, mainly in the severe cases in the 0–1y group. This could be helpful to support the implementation of this kind of strategy. Moreover, our work also highlights the importance of mathematical modeling of infectious diseases as a powerful tool to evaluate control strategies [18,33,34]. In particular, here we present a new methodology, applied to a deterministic, compartmental, and age-structured model, to assess the effect of delays in the primary pertussis vaccination schedule. However, this methodology (see details in Supplementary Material) could also be easily adapted to assess the impact of vaccination delays in other models that describe pertussis transmission or other infectious vaccinepreventable diseases.
Acknowledgements Data from vaccination on Flanders were kindly provided by Tine Lernout [21]. Data from Armenia [22] were taken of with permission of the authors. We thank Mario Arrúa, M.D., from Elina de la Serna Hospital for providing the vaccination data from the urban center of La Plata. We thank Mr. Jaime Alfredo Henen, PhD Belén Ozaeta, Mónica Sarijulis, M.D., and Valeria Forlani, M.D., from the Secretaría de Salud y Medicina Social de la Municipalidad de la Plata, for their permission and help with the collection of vaccination data from the suburban area of La Plata. This work was supported by Agencia Nacional de Promoción Científica y Técnológica (ANCPyT) grants PICT2010/0707(GF) and PICT2012/2719(DH). GF and PB are members of the Scientific Career of Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), DFH is a member of the Scientific Career of Comisión de Investigaciones Científicas de la Provincia de Buenos Aires (CICBA), PP is a fellow from ANCPyT.
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Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.vaccine.2015.07. 005 References [1] Edwards KM. Overview of pertussis: focus on epidemiology, sources of infection, and long term protection after infant vaccination. Pediatr Infect Dis J 2005;24:S104–8. [2] Williams GD, Matthews NT, Choong RK, Ferson MJ. Infant pertussis deaths in New South Wales 1996–1997. Med J Aust 1998;168:281–3. [3] Clark TA. Changing pertussis epidemiology: everything old is new again. J Infect Dis 2014;209:978–81. [4] Cherry JD. Epidemic pertussis in 2012 – the resurgence of a vaccine-preventable disease. N Engl J Med 2012;367:785–7. [5] Chiappini E, Stival A, Galli L, de Martino M. Pertussis re-emergence in the postvaccination era. BMC Infect Dis 2013;13:151. [6] Mooi FR, Van Der Maas NA, De Melker HE. Pertussis resurgence: waning immunity and pathogen adaptation – two sides of the same coin. Epidemiol Infect 2014;142:685–94. [7] Pertussis vaccines: WHO position paper. Releve epidemiologique hebdomadaire/Section d’hygiene du Secretariat de la Societe des Nations, vol. 85; 2010. p. 385–400. [8] Clark TA. Responding to pertussis. J Pediatr 2012;161:980–2. [9] Hozbor D, Mooi F, Flores D, Weltman G, Bottero D, Fossati S, et al. Pertussis epidemiology in Argentina: trends over 2004–2007. J Infect 2009;59: 225–31. [10] Falleiros Arlant LH, de Colsa A, Flores D, Brea J, Avila Aguero ML, Hozbor DF. Pertussis in Latin America: epidemiology and control strategies. Exp Rev Anti Infect Ther 2014;12:1265–75. [11] Romanin V, Agustinho V, Califano G, Sagradini S, Aquino A, Juarez MD, et al. Epidemiological situation of pertussis and strategies to control it: Argentina, 2002–2011. Arch Argent Pediatr 2014;112:413–20. [12] Winter K, Harriman K, Zipprich J, Schechter R, Talarico J, Watt J, et al. California pertussis epidemic, 2010. J Pediatr 2012;161:1091–6. [13] Kuehn BM. (ACIP): give pertussis vaccine during every pregnancy. JAMA 2012;308:1960. [14] Updated recommendations for use of tetanus toxoid, reduced diphtheria toxoid and acellular pertussis vaccine (Tdap) in pregnant women and persons who have or anticipate having close contact with an infant aged
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Mathematical modeling of delayed pertussis vaccination in infants P. Pesco a , P. Bergero a , G. Fabricius a,∗ , D. Hozbor b a Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, CC 16, Suc. 4, 1900 La Plata, Argentina b Laboratorio VacSal, Instituto de Biotecnología y Biología Molecular, Departamento de Ciencias Biológicas, Facultad de Ciencias Exactas, Universidad Nacional de La Plata y CCT-La Plata, CONICET, Calles 47 y 115, 1900 La Plata, Argentina
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Article history: Received 30 March 2015 Received in revised form 26 June 2015 Accepted 1 July 2015 Available online xxx Keywords: Pertussis Resurgence Delay in vaccination Mathematical model
a b s t r a c t Pertussis is an acute vaccine-preventable respiratory disease that remains a public health problem. In an attempt to improve the control of the disease, many countries have incorporated new boosters in their vaccination schedule. Since the incorporation of these boosters is relatively recent, there are not enough data about their impact to support and/or universalize their use. Alternative strategies such as the improvement in vaccine coverage and reduction in vaccination delays, in addition to the incorporation of boosters, could be implemented. Though these strategies are not new, they have not been adequately evaluated in order to be implemented and/or prioritized. To evaluate the potential impact of these alternative strategies on pertussis incidence, we developed a methodology that involves the use of data collected from vaccination centers and an age-structured deterministic mathematical model for pertussis transmission. The results obtained show that strategies that avoid delays in vaccination have a strong impact on incidence reduction in the most vulnerable population (infants less than 1y). In regions with high vaccination coverage (95%) the elimination of delays in the three primary doses decreases pertussis incidence in infants by approximately 20%. In regions where delays in the administration of vaccines are higher, the combined action to reduce delays and improve coverage leads to a significant improvement in disease control in infants. By repeating the calculations using different sets of parameters that describe different possible epidemiologic scenarios, we determined the robustness of our results. All the results presented highlight the importance of having high vaccine coverage and shorter delays in vaccine administration in order to reduce the impact of the disease in infants. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Pertussis is a highly contagious respiratory disease mainly caused by Bordetella pertussis. This disease, which causes uncontrollable violent coughing, most commonly affects infants and young children and can be fatal, especially in babies less than 1 year of age [1,2]. The best way to prevent pertussis is to get vaccinated. In fact, the introduction of massive pertussis vaccination in the fifties dramatically reduced the morbidity and mortality associated with the disease. However, in the last years the incidence rates of the disease have increased in many countries [3–6]. The World Health Organization estimates that about 16 million cases occur per year in the world with approximately 200,000 deaths [7]. Though most of these cases have been reported in countries with low
∗ Corresponding author. Tel.: +54 2214257430; fax: +54 2214254642. E-mail address: fabricius@fisica.unlp.edu.ar (G. Fabricius).
vaccination coverage, pertussis outbreaks were also detected in countries with high vaccination coverage [3,4]. In the Americas, the number of cases varies between 1500 and 49,000 among countries, where Argentina, Brazil, Mexico, Chile, Colombia, Paraguay, Peru, and the United States have reported the highest number of cases [8–10]. In Argentina, the last outbreak occurred in 2011 when 76 deaths were reported mainly in children under 6 months [11]. In 2012, in the US 48,778 cases (the highest outbreak since 1955) including 20 pertussis-related deaths were reported. Incidence rates were very high in infants but also in the population of children (7–10 years) and adolescents (13–14 years) [12]. This epidemiological situation has forced health systems to revise their control actions to strengthen and/or implement shortterm strategies to improve the situation, at least for the most vulnerable population represented by infants. Before the resurgence of the disease, recommended immunization schedules consisted of a primary series of 3 doses during the first year of life and a booster between 1 and 6 years of age, preferably during the second year of age. With the disease resurgence, more boosters
http://dx.doi.org/10.1016/j.vaccine.2015.07.005 0264-410X/© 2015 Elsevier Ltd. All rights reserved.
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were added following recommendations of international organizations [13–15]. In fact, the number of boosters increases year by year in many countries, probably as a consequence of failures in the used vaccines, in particular in acellular vaccines [16,17]. In this context, the evaluation of other alternative strategies, instead of the addition of the current acellular booster doses, is important for controlling the disease in the short term. In previous work, using an age-structured deterministic mathematical model for pertussis transmission designed by us, we estimated that improvements in the coverage of the first dose would lead to a larger reduction in the 0–1y disease incidence than that caused by the addition of an 11y booster [18]. The population dynamics of our model was described by transferring individuals among 9 epidemiological classes that differ in immune status and infectiousness. In the present work we evaluate the potential impact of shorter delays in the administration of the first three doses of pertussis vaccine on infants younger than 1y. With this aim, we developed a calculation method that involves the introduction of new epidemiological classes to keep track of the number of doses administered to the population in each epidemiological class. This method also allows us to accurately incorporate the vaccination coverage for each dose in the model. The results obtained with our model and data gathered from vaccination centers in urban and suburban areas in an Argentine city show that a reduction in delayed vaccination would decrease the incidence of the disease in infants by at least 20%. The results from the model reveal that efforts to improve the administration of the first doses of the immunization schedule, either by enhancing coverage or strictly complying with the recommended scheduled age, would significantly decrease pertussis incidence in infants. 2. Materials and methods 2.1. Vaccination schedule and epidemiological data In Argentina, the immunization schedule against pertussis includes three primary doses at 2, 4 and 6 months old, one booster dose at 18 months old, and another at 6 years (school entry) [19]. For all these doses, whole-cell pertussis vaccine is used (DTwP). According to the Ministry of Health, DTP3 coverage (DTP3-cov) for infants under 1y old was higher than 90%, but there are some regions with coverage below 80% [11]. Over the last few years, since the resurgence of pertussis, different protection strategies have been included in Argentina: immunization of adolescents, pregnant women and health workers with acellular vaccines. The epidemiological data included in this work, consisting of 29,845 records of pertussis vaccination for children aged 0–12 months, are from La Plata (654,324 inhabitants), an Argentinian city located in Buenos Aires province. Specifically, we used retrospective data (January 2005–May 2012) on the distribution of applied DTP doses by age provided by the vaccination center of Elina de la Serna Hospital. At this center, which is one of the 10 vaccination centers located in the urban region of La Plata city, approximately 13% of La Plata population is vaccinated. Children whose age was undefined or unclear were excluded. Fig. 1A shows the number of vaccinated individuals per dose by age from January 2005 to May 2012. In Fig. 1B we represent the same data as in Fig A, but as a fraction of vaccinated individuals at age ai with dose d (hereafter referred to as fdi ). These profiles were obtained by performing histograms with the data of Fig. 1A, where each histogram interval is taken as a month divided by four (a “week”), ages ai are assigned to the middle of the interval, and fdi are normalized to one for each dose, d. The fdi profiles and the vaccination coverages for each dose DTP-covd are the parameters that determine vaccine administration in our mathematical model.
Fig. 1. (A) Number of vaccinated individuals per dose by age, between January 2005 and May 2012 (continuous lines). Data are from Elina de la Serna Hospital. (B) Fraction of vaccinated individuals with dose d, at age ai (in weeks), fdi (gray lines are to guide the eye). Data are obtained from (A). In both figures dotted lines indicate the recommended age for primary doses of pertussis vaccination schedule in Argentina.
For comparison purposes, we also included epidemiological data from the periphery of La Plata city, where the population is younger than that from downtown, with 23% and 14% of inhabitants younger than 14 years old, respectively. There are 3.7 individuals per household on average, instead of the 2.7 individuals registered in the downtown area [20]. 2.2. Mathematical model The model used here to evaluate the effect of vaccination delays on pertussis transmission is based on a deterministic agestructured compartmental model developed previously by us [18]. The population dynamics of this model is described transferring individuals among 9 epidemiological classes at given rates as is shown in Fig. 2A. Each one of the 9 epidemiological classes is divided into age groups. To study the effect of delays in vaccination we have introduced modifications into the model that allow us to take into account the actual age at which the population receives the three primary doses of the pertussis vaccine, regardless of the age recommended by the national vaccination schedule. On the other hand, the fact that vaccination does not have a 100% effectiveness is considered assuming that only a fraction of
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Fig. 2. (A) Schematic representation of the basic epidemiological model. Individuals are born in the susceptible class S and remain there unless they become infectious through contact with an infected individual and enter the full symptomatic infective class I1 , or they acquire the lowest level of immunity (via the application of the first effective vaccine dose) and enter P1AI (PAI : Partial Acquired Immunity). When receiving successive effective vaccination doses (dotted lines), individuals go through classes of increasing immunity and eventually reach the CAI (Complete Acquired Immunity) class. Individuals in classes P1AI and P2AI develop a less symptomatic illness when they get infectious, entering class I2 (mild infection) or I3 (weak infection), respectively. Infection fades at a rate ␥ and individuals in classes I1 , I2 or I3 recover and enter R class. Waning immunity is considered by transferring population from classes R, CAI or PAI to classes of lower immunity at rates , , , respectively. Each epidemiological class is divided into age groups. (B) Disaggregation of S and PAI classes by applied doses. The subindex indicates the number of applied doses. The superindex in PAI classes determines the immunity level of the class and corresponds to the number of effective doses. Arrows represent population transfers when an effective (vertical) or ineffective (horizontal) dose of vaccine is applied. This increase in the number of epidemiological classes holds for age groups from 0 to 1y. For people older than 1y, discrimination of the population by the number of applied doses is not necessary and 9 epidemiological classes as in (A) are considered.
the individuals that received one dose of vaccine is transferred to an epidemiological class with a higher level of immunity. The rest of the individuals that after receiving the extra dose did not modify their immunological status are transferred to a new class that comprises a population of individuals with the same status of immunity but with an additional dose. In the previous model [18], when the dose was not effective, the individual remained in the original epidemiological class and no records of the number of doses administered were kept. Here this discrimination of transfer to another epidemiological class is necessary since the second dose is only given to individuals who have already received the first one (and the same for the third dose with respect to the second). The new compartments added to the model to account for this effect are shown in Fig. 2B. When an effective dose d is given at age ai , a fraction pdi *VE (of those moved due to aging) is transferred to an increased immunity class (indicated with vertical arrows in the figure). If the dose d is ineffective, a fraction pdi *(1-VE) is transferred to a class with the same level of immunity and one more dose given (horizontal arrow), while a fraction 1-pdi does not receive the dose and remains in the same class. Here, VE is the vaccine efficacy, pdi is the fraction of the aged ai population with d-1 doses that receives dose d at age ai , and is obtained from the fraction of vaccinated individuals by age fdi , and the corresponding vaccination coverage, DTPd-cov (computed as the fraction of infants vaccinated before 1y old). The set of ages ai is taken weekly from 2m to 1y (we assume each month has 4 weeks, a detailed explanation of the implementation of the vaccination procedure in the model is presented in the Supplementary Material). The dynamics of the model is described by a set of coupled nonlinear differential equations that are solved numerically to obtain the stationary state of the system. The incidences of the disease are then computed through expressions Inc1i = i (Si + S1i + S2i + S3i ),
1 1 1 Inc2i = i (PAI1 i + PAI2i + PAI3i )
where Inc1i and Inc2i are the incidences of fully and mild symptomatic pertussis cases, respectively for age group i. Inc1i is computed as the product of the force of infection i and the total population of susceptible individuals in the corresponding age group, which is composed of unvaccinated individuals (Si ) and vaccinated individuals with 1, 2 or 3 doses of vaccine that have been ineffective for them (S1i , S2i , S3i , respectively). Inc2i is computed in the same way, but the population considered is in the first
acquired immunity class as they have received 1 effective dose of vaccine. 3. Results For all calculations presented here, we considered the parameters corresponding to a previously defined CP1A-MDI scenario (see Ref. [18], where contact parameters obtained from forces of infection in the pre-vaccine era and intermediate values reported for the duration of pertussis immunity are considered). In the Supplementary Material, the complete set of parameters used in this work is presented, and the results obtained for other scenarios are discussed. 3.1. Assessment of the effect of delayed vaccination for different coverages The aim of this work is to assess the impact on the pertussis incidence in infants due to the reduction in the delays in DTP vaccination. With this purpose, we compared the incidences predicted by the model when the vaccination is delayed and when the recommended vaccination schedule is adhered to without any delay. To compute the 0–1y incidences in the case of delayed vaccination in our model, we included the weekly vaccination profile shown in Fig. 1B, and considered two possible values for DTP3-cov: 95% and 80%. To reach these coverages, we assume that DTP1-cov > DTP2-cov > DTP3-cov. We arbitrarily consider two sets: DTP1-cov = 99%, DTP2-cov = 97% DTP3-cov = 95%, and DTP1cov = 90%, DTP2-cov = 85%, DTP3-cov = 80%. As there are other possible combinations of coverages to reach the same DTP3-cov, we repeated the calculations for the case that all individuals that receive DTP1 also receive the following doses (DTP1-cov = DTP2cov = DTP3-cov, see Supplementary Material). Fig. 3 shows the incidences in the 0–1y group considering a delay in vaccination and the ideal situation without delay. As expected, when DTP3-cov = 95% and without delay, the predicted incidences are the lowest. When the delay is considered, both Inc1 and Inc2 increase. A similar trend is observed when DTP3cov = 80%. It should be noted that although no delayed vaccination is an unreal situation, the strategy of evolving from a stage DTP3cov = 80% with delay to a stage DTP3-cov = 95% without delay results in an incidence (Inc1 + Inc2 ) reduction of 39% with respect to the initial situation.
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26.7
Inc 2 Inc 1
23.6 19.7
20
10.7
16.2 15 10 5
12.5
11.3 9.1 12.9 7.1
8.4
Not Delayed
Delayed
14.2
0 DTP3-cov = 95%
Not Delayed
Delayed
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3
3.2. Assessment of some strategies for delay reduction In this section we evaluate different strategies to diminish the delays detected in the urban region (Fig. 1B, case I). For these calculations we considered DTP3-cov = 95%, as was reported for different urban areas of our country by Gentile et al. [23]. We first assessed the effect of completely avoiding the delay in the first dose (case II). The calculation shows that Inc1 + Inc2 remains as in case I (19.7 cases/year/100,000 inhabitants). However, reducing Inc1 (7.4 in case II instead of 8.4 in case I) at the expense of Inc2 (12.3 in case II vs. 11.3 in case I) decreases the number of severe pertussis cases. We also assessed the effect of avoiding the cumulative delays in DTP2 and DTP3 (case III). Here DTP1 is administered with delay, but with strict compliance with the recommended interval (2 months) between the following doses. As a result, Inc1 + Inc2 decreases by 13.9% with respect to case I, while a minor change for Inc1 results (3.3%). In case IV, DTP1 dose is administered as in case I, but the following doses are given without any delay, at the minimum interval between consecutive doses recommended by WHO. In this situation, as expected, the predicted Inc1 + Inc2 is slightly lower than that for case III (16.7 in case IV vs. 17.0 in case III) but higher than that for case V (16.7 in case IV vs. 16.2 in case V). Case V corresponds to no delayed vaccination, in which Inc1 and Inc2 decrease with respect to case I by 16.3% and 19%, respectively. This improvement is even higher (49.6% for Inc1 and 19% for Inc2 ) if only the 2–12m group, which is the one susceptible to be directly affected by vaccination, is considered (Table 1). 3.3. Assessment of the effect of changing the vaccination profile of a suburban area to that of an urban area In the suburban area of La Plata we detected a different vaccination profile with greater delays. The detail of the data is included in the supplementary material (Fig. S4). In Fig. 4 we show the agespecific coverage of DTP3 for the urban and suburban areas of La Plata and also include the ones for Flanders (Belgium) [21] and Armenia [22] to show that the delays detected in other regions are similar to those found in La Plata, or they could be even greater. To estimate the effect of the suburban-area delays on 0–1y pertussis incidence, we consider that the coverage for DTP3 is 87% instead of the 95% that we took for the urban area. We assume
La Plata (urban) La Plata (suburban) Flanders Armenia
0.2 0.1 0 100
DTP3-cov = 80%
Fig. 3. Effect of the delay on incidences Inc1 and Inc2 for DTP3-cov 95% and 80%. The numbers inside the bars indicate the Inc1 and Inc2 values, and the numbers above correspond to Inc1. + Inc2 . The label “Delayed” corresponds to the profile of Fig. 1(B), while the label “not delayed” corresponds to the case where all individuals receive the first, second and third vaccination doses at 2m, 4m and 6m, respectively.
3th dose
150
200
250
300
350
400
450
500
Age of immunization with DTP3 (days) Fig. 4. Age-specific coverage for DTP3 in La Plata, Argentina (urban and suburban areas). Data from Flanders (Belgium) [21] and Armenia [22] are shown for comparative purposes. The vertical line indicates the age of immunization recommended by the Argentinean and Armenian National Vaccination Schedules. The curve for Belgium was shifted 2 months to superimpose on the recommended age of vaccination in the other countries. La Plata urban data were obtained from Fig. 1(A), assuming DTP3-cov = 95%. For the suburban curve we included 1764 records of DTP vaccinations in infants between 0 and 12 months old obtained from Public Health Centers on the outskirts of La Plata (December 2012 and March 2013), assuming DTP3-cov = 87%.
DTP3-cov = 87% since from the information recorded in several vaccination centers of the suburban region, we found that 13% of the children who had completed their DTP3 vaccination dose received the third dose between 1 year and 3 years of age. Then, assuming that at the age of three 100% of the children received the DTP3 dose, at 1 year of age only 87% of the children have received the three recommended pertussis vaccine doses. If we assume that the proportions in such records are preserved in the whole suburban population, DTP3-cov should be at most 87%. The results of our calculations are shown in Fig. 5. When the delays in vaccination were reduced from those in the suburban profile (DTP3-cov = 87%) to the ones in the urban profile (DTP3-cov = 95%) of La Plata, a 27% decrease in Inc1 + Inc2 , 35.1% in Inc1 , and 19.5% in Inc2 was observed. In the figure we also included the results obtained for two other coverages for the suburban area: 80%, because this value can
Incidence (Cases/year per 100,000 population)
Incidence (Cases/year per 100,000 population)
30
Percentage of immunized individuals
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Inc2 Inc1
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30.4 27.0 23.7
20
19.7
15
11.3
14.5 14.0
13.5
10 13.0
5 0
DTP3−cov
8.4
Urban 95%
15.9
10.2
Suburban 95%
87%
80%
Fig. 5. Comparison of incidences Inc1 and Inc2 for the 0–1y age group for urban and suburban vaccination profiles of La Plata. DTP3-cov = 95% was used for the urban profile, while for the suburban profile three different DTP3-cov values were considered: DTP3-cov = 95% (higher than expected from the data), DTP3-cov = 87% (upper limit supported by current data) and the more realistic DTP3-cov = 80%. When DTP3cov = 87% we take DTP1-cov = 94.5% and DTP2-cov = 91%. For the other cases, we take the same coverages as in Section 3.1 for the first 2 doses.
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Table 1 Effect of the delay in the incidence by age for infants with less than 1y. Comparison of Inc1 and Inc2 values between delayed (Case I, Fig. 1(B)) and not delayed (Case V, Section 3.2) vaccination using DTP3-cov = 95%. DTP3-cov 95%
Inc1 Cases/year per 100,000 population
Age (m)
Delayed Case I
Not delayed Case V
Delayed Case I
Not delayed Case V
0–2 2–4 4–6 6–12 0–12
5.7 1.4 0.7 0.6 8.4
5.7 0.6 0.3 0.5 7.1
0.0 4.2 4.5 2.6 11.3
0.0 5.0 2.4 1.7 9.1
Inc2 Cases/year per 100,000 population
be detected in this region, as was reported by Gentile et al. [23], and 95%, which although not being realistic, from an academic point of view, it is interesting to separately observe the effects of coverage and delays when comparing them with those of the urban profile. The decrease in incidence predicted by the model in changing from a suburban to an urban profile was more pronounced than that resulting from the reduction in the urban profile up to fully compliance with the immunization schedule. In the Supplementary Material we discuss the robustness of our results considering different scenarios including the duration of immunity, the contact matrix, and vaccine effectiveness. 4. Discussion For pertussis and other vaccine-preventable diseases, the delay in the acquisition of immunity through late immunization could negatively impact on the disease transmission [24–27]. In fact, it is generally accepted that immunization at the earliest appropriate age is an important public health goal. Several countries such as US, Sweden and Australia have reported age properly immunized around 48–75% [28]. In Argentina, delay in vaccination was also detected in different populations [29–31]. The impact of delayed vaccination on the incidence of pertussis has been scarcely studied, and the effect of reducing it is even less known [24,32]. In this work, we assessed the impact on the incidence in the most vulnerable group due to the reduction in the delays of the primary doses of pertussis vaccine. With this aim, we used an age-structured deterministic mathematical model for pertussis transmission and data collected from an urban vaccination center in Argentina. With our model, we evaluated the impact of completely avoiding the delays in each one of the three recommended primary doses for pertussis control. The results show that incidence reduction is important for both analyzed coverage: 95% (adequate) and 80% (suboptimal), being more noticeable in the first coverage scenario. Avoiding delays in the administration of primary doses would have a different impact on the 0–2m group than on the 2–12m group. As expected, in the 0–2m group the impact of reducing the delays is hardly noticeable (only reduction due to herd immunity, which in this case is low) since this age group is not given any vaccine according to immunization schedules like that of Argentina. For the 2–4m group no delays decrease the number of severe cases (Inc1 decreases by 56.4% for 95% coverage) and for the 4–6m and the 6–12m groups with 95% coverage, Inc1 + Inc2 decreases up to 48.5% and 31.1%, respectively. Although this reduction in delayed vaccination up to full compliance with the immunization schedule seems highly unlikely due to the numerous uncontrollable reasons that may cause it [29,31], our results point out the magnitude of the improvement that could be achieved by implementing such health-care actions. Our method also allowed us to analyze other strategies that could be more easily implemented by the health system. Thus, we observed that when there are no delays in DTP1 administration, although the total incidence cannot be decreased,
the total number of severe cases is lower (lower Inc1 at the expense of Inc2 ). This strategy should be recommended by pediatricians to newborns’ parents. Moreover, when delays are not cumulative (i.e., when after the first dose the 2 month interval is strictly preserved) Inc1 + Inc2 decreases by 13.8%. Comparatively, the elimination of the vaccination delays in both the second and third doses causes a smaller effect on incidence reduction, mainly affecting the Inc2 value. This strategy should be mainly recommended by vaccinators. We could also observe that when the delay in suburban areas could be reduced to those in the urban area, a reduction of 27% in Inc1 + Inc2 could be detected. Although the delays and profiles we worked with are from Argentina, they are comparable to those in other countries, as shown in Fig. 4. The robustness of our results was tested by repeating the calculations using different sets of parameters allowing us to extend our conclusions to other possible epidemiological scenarios (Supplementary material). All these results undoubtedly show that the reduction in the delays has a positive impact on incidence reduction, mainly in the severe cases in the 0–1y group. This could be helpful to support the implementation of this kind of strategy. Moreover, our work also highlights the importance of mathematical modeling of infectious diseases as a powerful tool to evaluate control strategies [18,33,34]. In particular, here we present a new methodology, applied to a deterministic, compartmental, and age-structured model, to assess the effect of delays in the primary pertussis vaccination schedule. However, this methodology (see details in Supplementary Material) could also be easily adapted to assess the impact of vaccination delays in other models that describe pertussis transmission or other infectious vaccinepreventable diseases.
Acknowledgements Data from vaccination on Flanders were kindly provided by Tine Lernout [21]. Data from Armenia [22] were taken of with permission of the authors. We thank Mario Arrúa, M.D., from Elina de la Serna Hospital for providing the vaccination data from the urban center of La Plata. We thank Mr. Jaime Alfredo Henen, PhD Belén Ozaeta, Mónica Sarijulis, M.D., and Valeria Forlani, M.D., from the Secretaría de Salud y Medicina Social de la Municipalidad de la Plata, for their permission and help with the collection of vaccination data from the suburban area of La Plata. This work was supported by Agencia Nacional de Promoción Científica y Técnológica (ANCPyT) grants PICT2010/0707(GF) and PICT2012/2719(DH). GF and PB are members of the Scientific Career of Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), DFH is a member of the Scientific Career of Comisión de Investigaciones Científicas de la Provincia de Buenos Aires (CICBA), PP is a fellow from ANCPyT.
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Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.vaccine.2015.07. 005 References [1] Edwards KM. Overview of pertussis: focus on epidemiology, sources of infection, and long term protection after infant vaccination. Pediatr Infect Dis J 2005;24:S104–8. [2] Williams GD, Matthews NT, Choong RK, Ferson MJ. Infant pertussis deaths in New South Wales 1996–1997. Med J Aust 1998;168:281–3. [3] Clark TA. Changing pertussis epidemiology: everything old is new again. J Infect Dis 2014;209:978–81. [4] Cherry JD. Epidemic pertussis in 2012 – the resurgence of a vaccine-preventable disease. N Engl J Med 2012;367:785–7. [5] Chiappini E, Stival A, Galli L, de Martino M. Pertussis re-emergence in the postvaccination era. BMC Infect Dis 2013;13:151. [6] Mooi FR, Van Der Maas NA, De Melker HE. Pertussis resurgence: waning immunity and pathogen adaptation – two sides of the same coin. Epidemiol Infect 2014;142:685–94. [7] Pertussis vaccines: WHO position paper. Releve epidemiologique hebdomadaire/Section d’hygiene du Secretariat de la Societe des Nations, vol. 85; 2010. p. 385–400. [8] Clark TA. Responding to pertussis. J Pediatr 2012;161:980–2. [9] Hozbor D, Mooi F, Flores D, Weltman G, Bottero D, Fossati S, et al. Pertussis epidemiology in Argentina: trends over 2004–2007. J Infect 2009;59: 225–31. [10] Falleiros Arlant LH, de Colsa A, Flores D, Brea J, Avila Aguero ML, Hozbor DF. Pertussis in Latin America: epidemiology and control strategies. Exp Rev Anti Infect Ther 2014;12:1265–75. [11] Romanin V, Agustinho V, Califano G, Sagradini S, Aquino A, Juarez MD, et al. Epidemiological situation of pertussis and strategies to control it: Argentina, 2002–2011. Arch Argent Pediatr 2014;112:413–20. [12] Winter K, Harriman K, Zipprich J, Schechter R, Talarico J, Watt J, et al. California pertussis epidemic, 2010. J Pediatr 2012;161:1091–6. [13] Kuehn BM. (ACIP): give pertussis vaccine during every pregnancy. JAMA 2012;308:1960. [14] Updated recommendations for use of tetanus toxoid, reduced diphtheria toxoid and acellular pertussis vaccine (Tdap) in pregnant women and persons who have or anticipate having close contact with an infant aged
